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Representation of the Characteristic Temperature of Correlative Thermal Conductivity of Opacifier-Fiber Doped Silica Aerogel by Steady-State Method at Large Temperature Differences

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Abstract

To evaluate the thermal insulation performance of opacifier-fiber silica aerogel at large temperature differences (ΔT > 100 K), this study proposes a characteristic temperature method to represent the thermal conductivity measured by the steady-state method. The theoretical temperature-dependent thermal conductivity model of opacifier-fiber doped silica aerogel is first proposed, including the thermal conductivity model of heat conduction and radiation. Then, the characteristic temperature is conducted based on Fourier’s law and their temperature-dependent thermal conductivity model, and the key parameters are obtained. The results indicate that the correlative thermal conductivity of silica aerogel with 1 % SiC & 0.51 % fiber and 5.84 % SiC & 0.51 % fiber equal 0.03105 to 0.03998 and 0.03181 to 0.03685 W·m−1·K−1, respectively, at ΔT = 136 K to 799 K and Tc = 288 K. Specifically, the characteristic temperature representation method is more efficient and accurate to represent the correlative thermal conductivity measured by the steady-state method at large ΔT than the standard method of (Th + Tc)/2, where the accuracy can be upgraded by 6.88 %.

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Abbreviations

A:

Specimen’s cross-section area

cp :

Specific heat, J·kg−1·K−1

C:

Gas coefficient

C0 :

A factor of the characteristic temperature of λa

C1 :

A factor of the characteristic temperature of λa, W·m−1·K−2

C2 :

A factor of the characteristic temperature of λa, W·m−1·K−3

C3 :

A factor of the characteristic temperature of λa, W·m−1·K−4

C4 :

A factor of the characteristic temperature of λr, W·m−1·Kγ−4

D:

Particle diameter size, μm

I:

The electric current, I

lg :

Gas molecules mean free path

P:

Pressure, Pa

q:

Heat flux, W·m−2

t:

Time, s

T:

Temperature, K/°C

U:

Voltage, V

δ :

The thickness of the specimen, m

γ :

A factor of the characteristic temperature of λr

ΔT :

Temperature difference, K

φ :

Volume fraction

λ :

Thermal conductivity, W·m−1·K−1

λ′:

Spectrum

ρ :

Density, g·cm−3

ρ b :

Density of the skeleton, g·cm−3

σ :

Stefan-Boltzmann constant, W·m−2·K−4

a:

Aerogel

ao :

Opacifier doped silica aerogel

b:

Black-body

c:

Cold surface

cd:

Heat conduction of silica aerogel composite

e:

Effective

ext:

Extinction

f:

Fiber

g:

Gaseous-contributed

h:

Hot surface

op:

Opacifier

r:

Radiation

s:

Solid-contributed

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Acknowledgments

This work was supported financially by the Innovation Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00020) and the National Natural Science Foundation of China (No. 52006243).

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Authors and Affiliations

  1. School of Materials Science and Engineering, Shanghai University, Shanghai, 200444, People’s Republic of China

    Hao-Qiang Pang & Yan-Feng Gao

  2. College of Energy, Soochow University, 333 East Ganjiang Road, Suzhou, 215031, People’s Republic of China

    Ting-Hui Fan

  3. College of New Energy, China University of Petroleum (East China), Qingdao, Shandong, People’s Republic of China

    Chuan-Yong Zhu

  4. College of Engineering, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing, 10087, People’s Republic of China

    Tian-Yuan Liu

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Pang, HQ., Fan, TH., Zhu, CY. et al. Representation of the Characteristic Temperature of Correlative Thermal Conductivity of Opacifier-Fiber Doped Silica Aerogel by Steady-State Method at Large Temperature Differences. Int J Thermophys 43, 150 (2022). https://doi.org/10.1007/s10765-022-03068-z

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